QHrider, there is nothing to stop you from trying it!! You will absolutely love it. I call it rodeo in an english saddle.
Your cow horses could do it just fine, too. I was brought a roping horse to work with. He could not pick up one of his leads do to all the years just roping. He was a true bull-dog style QH. I did dressage with him to balance him and make him flexible. He loved dressage. So, one day I asked the owner if I could pop him over a jump or two. Sure, she says. Well, several months later he won his first beginner novice event.
He was the most unlikely event horse, if you just went by looks. The difference was, he had a heart the size of Texas and would do anything for you.
Here is Toby in his first event with me in Colorado;
Not bad at all, Allison! My roping mare has bursts of brilliance... she too doesn't want to pick up her right lead in an arena, but when I ask her to go after a cow, her leads are swapping constantly cause she's anticipating what's going to happen.
Sure, why not? We found a potato field and had a fight, on horseback, with potatoes that missed getting harvested. It was interesting.... 8 people running around at a gallop throwing potatoes at each other. By the time the day was done, the horses were pretty bombproof!